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Intonation in a new composition in 19-tone equal temperament Richard Parncutt Department of Musicology University of Graz, Austria Graham Hair Department of Music & Centre for Music Technology Umiversity of Glasgow, Scotland Presented at CIM08, Thessaloniki Musical pitch categories • apply to both relative and absolute pitch • typical tolerance: + half category width Chromatic scale, equal temperament (12ET): • tolerance = + quarter tone • learned from experience (e.g. piano) Literature Burns, E. M., & Ward, W. D. (1978). Categorical perception - phenomenon or epiphenomenon: evidence from experiments in the perception of melodic musical intervals. Journal of the Acoustical Society of America, 63, 456-468. Siegel, J. A., & Siegel, W. (1977). Absolute identification of notes and intervals by musicians. Perception & Psychophysics, 21 (2), 143-152. Data of Burns Microtonal scales • >12 pitch categories per octave • perceptually analogous to 12ET Hypotheses: • category centers, widths can be learned • typical tolerance: + half category width • scalar bilingualism is possible – retune internal representation – juxtapose two internal representations Inspiration: Kopiez (2003) • accompaniment: either ET or pure/just • solo: ~ET in both cases Intonation (deviation from ET) depends on – specific interval – musical structure – instrumental limitations Kopiez, R. (2003). Intonation of harmonic intervals: Adaptability of expert musicians to equal temperament and just intonation. Music Perception, 20, 383-410. Microtonal composition • Substantial minority tradition • Wide range of systems • Favored instruments: keyboard, fretted strings, mallet percussion, mechanically tuned electronic, computer No tradition develops perceptual performance skills of musicians! 19ET • Smallest interval: 1:21/19 • Closely approximates small-integer ratios • Assumption: – easiest microtonal system to perceive and perform Mandelbaum, J. (1961). Multiple division of the octave and the tonal resources of 19-tone temperament. Unpublished PhD Dissertation, University of Indiana. 19ET 19ths above C 0 notation cents above C 1 2 3 4 5 6 C C# Db D D# Eb E 0 63 126 189 253 316 379 7 8 E#/Fb F 442 505 Our notational rule: sharp (#) = +1/19 flat (b) = -1/19 Aims • Develop microtonal… – composition tradition and skills – performance tradition and skills • Document how musicians adapt… – thinking – perception – performance Method • Participants • Materials – music – equipment • Procedure Participants Clarinettist: Dr. Ingrid Pearson • Regular performances at UK national level in/with early music ensembles – Hanover Band, Gabrieli Consort and Players, Orchestra of the Age of Enlightenment, English Baroque Soloists, English Concert, Symphony of Harmony and Invention. • Deputy director, graduate school, RCM London Soprano: Amanda Morrison • Regular performances at UK national level in/with vocal ensembles • Synergyvocals, BBC Singers, Steve Reich and Musicians, Scottish Voices, Tallis Scholars, The Sixteen, Monteverdi Choir, Crafty Musick, Gesualdo Consort of London, Exaudi The music • Three short 19ET songs @ 1 minute • Voice, clarinet, keyboard • Composer: Graham Hair Graham Hair: 3 microtonal songs Radical Simplicity • reaction against modernist complexity • helps singers, instrumentalists achieve 19ET Inspiration: • Harry Partch: • Erik Satie: • John Cage: “17 Lyrics of Li-Po” “Socrate” "Cheap Imitation“ – itself based on "Socrate“ Cage: Hair: chromatic modality hyperchromatic modality Equipment • 19-ET keyboard – scordatura (re-tuned) – keyboard is 12ET, sound is 19ET • 19ET keyboard tablature – conventional notation – helps pianist put fingers on right keys • Pitch-tracking software (Rosegarden) – Listens to performers – Feedback on microtonal accuracy Procedure – Practice and rehearsal • soloists alone – with recording of accompaniment – with pitch tracker software • with composer as co-repetiteur – at 19ET keyboard final revisions of score – Recording • with keyboard accompaniment • separate tracks for each instrument/voice – Frequency measurement • of separate tracks for soprano and clarinet Practice time • about 4 hours at home • about 4 hours rehearsal with composer • recordings of "Wine" and "Dance" – sop and clar separately – about 40 takes in 4 hours – criterion for choice of takes to analyse: • best overall performance • most in tune according to composer • most in tune according to real-time pitch tracker Frequency measurement 1. Divide time axis into frames • frame length: 1024 samples = 1/43 s 2. Each frame one frequency • autocorrelation? • FFT? • harmonic spectral product? 3. Assign frequencies to 5-cent bins • 240 bins in 1 octave, 440-880 Hz no. of frequencies falling in each 5-cent bin Wine, bars 1-9, clarinet First peak: 1= 1/19 octave 63 = 63 cents 9 568 5 316 2 126 7 442 1 63 4 253 3 189 13 821 16 1011 15 947 12 758 6 8 379 505 14 884 18 17 1074 1137 10 11 631 695 Log of center frequency of bin (0 cents = 440 Hz) Tentative results • Singers and instrumentalists can learn 19ET – emulating 12ET-categorical perception/performance • Practice time is reasonable – with appropriate computer and personal support • Further improvement is expected – with practice time (cf. expertise research) • Scalar bilingualism – a realistic goal Implications Scalar bilingualism • enormously broadens compositional possibilities Microtonal music can become mainstream • if one system is used consistently • with large repertoire and sustained tradition